01 - Combine shredded chicken breast with BBQ sauce in a medium bowl, tossing until evenly coated throughout.
02 - Lay out sourdough slices and spread softened butter on one side of each slice. Place bread butter-side down on preparation surface.
03 - Place cheddar slice on 4 buttered bread slices. Top with BBQ chicken mixture, red onion slices, pickled jalapeños, mozzarella slice, and remaining cheddar slice. Complete with second bread slice, buttered side facing outward.
04 - Heat large skillet or griddle over medium heat. Cook sandwiches for 3–4 minutes per side, pressing gently with spatula until bread achieves golden-brown color and cheese melts completely.
05 - Remove from heat, cut each sandwich diagonally in half, and serve immediately while hot.